理论力学：静力学（双语一）：第一章静力学基本公理和物体的受力分析

1Theoretical Mechanics23IntroductionStatics is the branch of mechanics which studies the laws ofequilibria of bodies under the action of force systems,It mainly studies simplifications and equilibrium conditionsof force systems and applications of the corresponding results,4静力学主要研究：力系的简化和力系的平衡条件及其应用。引 言静力学是研究物体在力系作用下平衡规律的科学。5Theoretical mechanics67§ 1–1 Fundamental concepts in statics§ 1–2 Principles of statics§ 1–3 Constraints and their reaction forces§ 1–4 Force analysis and force diagramsChapter 1,Fundamentalprinciples of statics and force analysis8§ 1–1 静力学的基本概念§ 1–2 静力学公理§ 1–3 约束与约束反力§ 1–4 物体的受力分析与受力图第一章 静力学公理与物体的受力分析9Chapter 1,Fundamentalprinciples of statics and force analysis§ 1-1 Fundamental concepts in statics1,Force1) Concept,the mechanical interaction of bodies is caused byforces,This interaction can change the state of motion of abody,2) Effects of forces,① motion (external effect)② deformation (internal effect),3) The three elements,magnitude,direction andpoint of application,A F4) Unit of force,newton (N) (International System of Units)kilonewton (kN)10力的单位,国际单位制：牛顿 (N)千牛顿 (kN)第一章 静力学基本公理和物体的受力分析§ 1-1 静力学基本概念一、力的概念1．定义, 力是物体间的相互机械作用,这种作用可以改变物体的运动状态。2,力的效应,① 运动效应 (外效应 ) ② 变形效应 (内效应 )。3,力的三要素,大小，方向，作用点 A F11Force system,a group of forces acting on a body,Balanced force system,if a body subjected to aforce system is in equilibrium state,we call the system to be a balanced,A body is called to be in the state of equilibrium if it does not moveor if it moves with an uniform velocity,2.Rigid bodyA body which does not change its shape and dimension underapplied forces is called a rigid body3.Equilibrium stateAF12力系,是指作用在物体上的一群力。平衡力系,物体在力系作用下处于平衡,我们称这个力系为平衡力系。是指物体相对于惯性参考系保持静止或作匀速直线运动的状态。二,刚体就是在力的作用下，大小和形状都不变的物体。三,平衡AF13§ 1-2 Principles of staticsPrinciples,conclusions obtained from longtime practice and frommany experiments,They are repeatedly proved by practice and noware recognized without prove,1st Principle,two force equilibriumA rigid body subjected to the action of two forces can be inequilibrium,the necessary and sufficient conditions are,the two forces are equal in magnitude,| F1 | = | F2 |the two forces are opposite in direction,F1 = –F2the two forces are collinear,the two forces act on the same body,14§ 1-2 静力学基本公理公理,是人类经过长期实践和经验而得到的结论，它被反复的实践所验证，是无须证明而为人们所公认的结论。公理 1 二力平衡公理作用于刚体上的两个力，使刚体平衡的必要与充分条件是,这两个力 大小相等 | F1 | = | F2 |方向相反 F1 = –F2作用线共线,作用于同一个物体上。15Explanation,① As far as rigid bodies are concerned,the conditions above arenecessary and sufficient,② As far as deformable bodies are concerned,the conditionsabove are only necessary,bodies (deformable body) string二力杆Double forceequivalent bodyDouble forceequivalent rod③ double force equivalent body,is a rigid body subjected totwo forces must be in equilibrium,16说明, ①对刚体来说，上面的条件是充要的③ 二力体,只在两个力作用下平衡的刚体叫二力体。② 对变形体来说，上面的条件只是必要条件 (或多体中 )二力杆17The action of a given force system on a rigid body remains unchangedif another balanced force system is added to or subtracted from theoriginal system,Corollary 1,transmissibility of a forceThe point of application of a force acting on a rigid body can betransferred to any other point on the line of action of the force withoutaltering its effect,Therefore,as far as a rigid body is concerned,a force can becharacterized by three elements,magnitude,direction and line ofapplication,2nd Principle,addition and subtraction of balanced force systems18在已知力系上加上或减去任意一个平衡力系，并不改变原力系对刚体的作用。推论 1：力的可传性。作用于刚体上的力可沿其作用线移到同一刚体内的任一点，而不改变该力对刚体的效应。因此，对刚体来说，力作用三要素为,大小，方向，作用线公理 2 加减平衡力系原理19If a free rigid body remains in equilibriumunder the action of three nonparallel coplanarforces,the lines of action of those forcesintersect at one point,Moreover,three forces arecoplanar,(under special circumstances,forcesintersect at infinite and become aparallel force system),3rd principle,the law of parallelogramCorollary 2,three equivalent forces intersectat one point21 FFR ??Two forces applied at one point of a bodyhave as their resultant a force applied at thesame point and represented by the diagonalof a parallelogram constructed with twogiven forces as its sides,20刚体受三力作用而平衡，若其中两力作用线汇交于一点，则另一力的作用线必汇交于同一点，且三力的作用线共面。（ 必共面，在特殊情况下，力在无穷远处汇交 —— 平行力系 。）公理 3 力的平行四边形法则作用于物体上同一点的两个力可合成一个合力，此合力也作用于该点，合力的大小和方向由以原两力矢为邻边所构成的平行四边形的对角线来表示。推论 2,三力平衡汇交定理21 FFR ??214th principle,the law of action force and reaction forceTo any action of one material body onanother there is always an equal andoppositely directed reaction,They areequal in magnitude,opposite indirection,collinear and exist together,but act on different body,Prove,∵ is a balanced force system,∴ is a balanced force system too,again∵ If two forces are in equilibrium,they must be equal in magnitude,opposite in direction and collinear,∴ intersect at a point and are coplanar,321,,FFF321,,FFF3,FRExampledropletThe force the droplet acton the stringThe force the string acton the dropletGravitationThe reaction force of p22公理 4 作用力和反作用力定律等值、反向、共线、异体、且同时存在。[证 ] ∵ 为平衡力系,∴ 也为平衡力系。又 ∵ 二力平衡必等值、反向、共线,∴ 三力 必汇交，且共面。321,,FFF321,,FFF3,FR[例 ] 吊灯235th principle,principle of solidificationIf a deformable body subjected to the action of a force system is inequilibrium,the state of equilibrium will not be disturbed if thebody solidifies(becomes rigid)The 5th principle tells usthat the equilibrium of abalanced deformable bodycan be described by thetheory for a rigid body,Soft stringdrawdrawSolidified rigid roddrawdraw24公理 5 刚化原理变形体在某一力系作用下处于平衡，如将此变形体变成刚体（刚化为刚体），则平衡状态保持不变。公理 5告诉我们：处于平衡状态的变形体，可用刚体静力学的平衡理论。25§ 1-3 constraints and their reaction forces1,ConceptsFree body,A body not connected with other bodies and capableof displacement in any direction is called a free body,Constrained body,A body whose displacement in space is restricted byother bodies,either connected to or in contact with it,is called a constrained body,Constraint,Anything that restricts the displacement of a givenbody in space.(here,constraint is a noun,not a verb),Reaction force of a constraint,The force by which a constraint acts on a body,therebyrestricting its displacements,is called the force ofreaction of the constraint,26约束反力,约束给被约束物体的力叫约束反力。§ 1-3 约束与约束反力一、概念自由体,位移不受限制的物体叫自由体。非自由体,位移受限制的物体叫非自由体。约束,对非自由体的某些位移预先施加的限制条件称为约束。（这里，约束是名词，而不是动词的约束。）27① their magnitude is usually unknown;② their direction is always opposite to the direction in whichthe given constraint prevents the displacement of the body;③ the point of application is the contact point between thebody and the constraint,The characteristics of reaction force of constraints,G GN1N228① 大小常常是未知的；②方向总是与约束限制的物体的位移方向相反；③作用点在物体与约束相接触的那一点。约束反力特点,G GN1N229Strings can only be stretched,therefore the reaction force appliesat the point of contact and the direction of it is away from thebody,2,Some common types of constraints and their reactionforce direction,1) Constraints given by a string,a chain or a strapP PT S1 S'1S'2 S230绳索类 只能受拉,所以它们的约束反力是 作用在接触点,方向 沿绳索背离物体 。二、约束类型和确定约束反力方向的方法,1.由柔软的绳索、链条或皮带构成的约束P PT S1 S'1S'2 S231the reaction force is applied at the point of contact and directednormal to both surfaces,2) Smooth contact plane (smooth,not taking friction into account )PN NPNANBCommon normalCommontangent32约束反力 作用在接触点处,方向 沿公法线，指向受力物体2.光滑接触面的约束 (光滑指摩擦不计 )PN NPNANB333) Smooth cylindrical pin① cylindrical pinPin343.光滑圆柱铰链约束① 圆柱铰链35A XAYAAADirection is uncertainMagnifiedpicturePin36AAXAYAA37② fixed hinged support38② 固定铰支座39fixed hinged support40固定铰支座41runner and pin(double surfaceconstraints)42滑槽与销钉（双面约束）43double forceequivalent rod44二 力 杆45Kinetic hinged support (step bearing)The actualdirection of N canbe downward,46活动铰支座（辊轴支座）N的实际方向也可以向下47Kinetic hinged support (step bearing)48活动铰支座（辊轴支座）491,Force analysisTo solve a problem of statics,First select the body to be studied,Secondly,in accordance with the given conditions and constraints,analyze the forces which act on the bodies using the basic conceptsand principles,This process is called force analysis,The forces acting on a body can be classified as,1,active forces,such as the gravitational force,the force of windpower,the pressure of gases,etc,2,passive forces,such as reaction force of constraints,§ 1-4 Force analysis and force diagrams50一、受力分析解决力学问题时，首先要选定需要进行研究的物体，即选择研究对象；然后根据已知条件，约束类型并结合基本概念和公理分析它的受力情况，这个过程称为物体的 受力分析 。作用在物体上的力有：一类是,主动力,如重力,风力,气体压力等。二类是：被动力，即约束反力。§ 1-4 物体的受力分析和受力图51The main steps to draw the force diagrams,① select the object under study;② divide the object into several parts andstudy the parts one by one;③ draw the active forces;④ draw the reaction force of the constraints,2,Force diagrams[Example 1]52画物体受力图主要步骤为,①选研究对象；②取分离体；③画上主动力；④画出约束反力。二、受力图[例 1]53[Example 2] Please,draw the force diagrams forall components in the picture,Q AOBCDERod54[例 2] 画出下列各构件的受力图Q AOBCDE55Q AOBCDE56Q AOBCDE57Q AOBCDE58Q AOBCDE59[Example 3] Please,draw the force diagrams forall components in the picture,Notice,three balanced forcesmust intersect at a point,Butif they are parallel,theyintersect at infinity,This is aspecial case,60[例 3] 画出下列各构件的受力图说明：三力平衡必汇交当三力平行时，在无限远处汇交，它是一种特殊情况 。61[Example 4] Sharp point contactsGet rid of constraints Get rid of constraints62[例 4] 尖点问题应去掉约束 应去掉约束63[Example 5] Please,draw the force diagrams forall components in the picture,64[例 5] 画出下列各构件的受力图653,Some problems which should be taken into account whendrawing a force diagram,Mutual mechanical action forces exist,only ifbodies contact,except for gravitation andelectromagnetic force,So the bodies which arein contact with the object under study should bemade clear,There must have force at the contactpoint,the direction of the force depends on thetype of constraints,Mind you,the force is the mutual mechanicalaction between bodies,Thereby,every force thebody subjected,relatives to a body who appliesthe force,We should make it clear,1) Don’t leaveout any force2) Don’t drawredundantforce66三、画受力图应注意的问题除重力、电磁力外，物体之间只有通过接触才有相互机械作用力，要分清研究对象（受力体）都与周围哪些物体（施力体）相接触，接触处必有力，力的方向由约束类型而定。2、不要多画力要注意力是物体之间的相互机械作用。因此对于受力体所受的每一个力，都应能明确地指出它是哪一个施力体施加的。1、不要漏画力67The direction of constraint reaction force must be strictlyaccording to the type of constraint,never be simply supposedby direct-view or the direction of the active force,Whenanalyzing the action forces and the reaction forces betweentwo bodies,please give attention to the direction of the forces,If the direction of the action force has been determined,thedirection of the reaction force is opposite to the action force,Don’t draw the direction of forces wrong,3) Don’t draw the direction of force wrong4) There are no constraints on the force diagramsThe force diagrams can be draw only on a part of the object,68约束反力的方向必须严格地按照约束的类型来画，不能单凭直观或根据主动力的方向来简单推想。在分析两物体之间的作用力与反作用力时，要注意，作用力的方向一旦确定，反作用力的方向一定要与之相反，不要把箭头方向画错。3、不要画错力的方向4、受力图上不能再带约束。即受力图一定要画在分离体上。69Whether a force is an external force or an internal one dependon the special objects,When a body system is divided intoseveral parts,some internal forces of old system may turn intothe external forces of the new object under study,If the direction of the reaction force of a constraint is defined,itshould be kept to the same in the analysis of the whole body asin the analysis of the components,5) no internal forces but only external forces can be drawn ona force diagram6) The force diagram for the whole object should be inaccordance with the force diagrams for any part,theyshould assort with each other,but not conflict,7) Make a exact judge for the double forces components,70一个力，属于外力还是内力，因研究对象的不同，有可能不同。当物体系统拆开来分析时，原系统的部分内力，就成为新研究对象的外力。对于某一处的约束反力的方向一旦设定，在整体、局部或单个物体的受力图上要与之保持一致。5、受力图上只画外力，不画内力。6,同一系统各研究对象的受力图必须整体与局部一致，相互协调，不能相互矛盾。7,正确判断二力构件。7172